The concept of non-existant truth is particularly useful in social sciences. A vast part of things that affect on our lives are created by humans itself and these things do not exist by themselves e.g. responsibility, moral and laws.
It should be clear that denying these things is likely to cause remarkable problems to a coherent nihilist.

From historical point of view nihilism was exercised by some Russian university students late 1800's who were thought to be part of the upper class. They rejected all or the most of the values of present society. Punk was a very nihilistic movement before it was recuperated. Punk was an absolute denial of music and taste of trends, expressed by shitty outfit. The self-destructive lifestyle of punks can be labelled nihilistic.

Nihilism faces a lot of the same problems that other philosophies face, however, due to its inherent destructiveness, and subsequent alienation, many of these are ignored. To take an example, lets look at josmos's wu above (which I must say is very well written), and see if we can approach it in a more balanced manner.

Now, moving on from semantics, lets look at the coin toss analogy. This is here to demonstrate to us the unknowability of truth in a probabilistic framework. Unfortunately, while the analogical truth that one cannot know what outcome will occur at the toss of a coin is logically true, this also implies that should the coin fall within certain measurable parameters (IE be approximately close to the fair ideal of a coin) then empirical observation has revealed always in the past a converging of the outcomes of heads/tails at half/half. It is reasonable to assume that unless anything else changes, that this will continue. You see, the logic here isn't dealing is specific outcomes, per se, but the whole system, which can be said to follow observable, and reliable behaviour. It can only do this if the smaller component behaviours of it's elements combine to form the regular system we observe. The truth of the maxim isn't lost in the individual coin toss, it emerges over the series of coin tosses, and the larger the series, the more true it will be.

Faith does not equal fact.

This paragraphs still makes the same 'mind in error' assumption as before. If our minds are in error, then how do we know this? In fact what are we to compare against? A truth? An Objective reality? It's like one domino leaning on it's friends for support, if you push one, they all fall down, because they're all the same. If you assume universal subjectivity, you can't then call into error it's conclusions, because you have nothing (pun intended) to compare them with.

Yes it is, as long as you always see it that colour, and call it the same thing, and it matches what other people call green in life, then you're fine. The 'subjective' reality of the colour as you percieve it makes no difference to it's logical properties, or indeed to logic itself. The neat thing here is the assumption that there *is* a right from which one is falling short. I would argue that the notion of nihilism here is emerging from a confusion between subjective and objective rather than anything substantial.

On logic and axioms...

One cannot have logic without axioms, or indeed any formal system. However there seems to be a misunderstanding about the axioms, which are in themselves abstractions of concepts observed to be working in real life. They're put side by side with others like them to see if they're consistent with each other, and whether it's possible to deduce anything useful from them. This doesn't change their objectivity, nor does it make them 'faith', they are genuinely useful in that they help us achieve specific goals. We question them regularly, because, like all science, truths are discovered, not made up.

Cogito Ergo Sum

Maybe, but we could define 'am' the usual way, and say it means to exist, now. Though the bulk of philosophical work has been trying to discover what 'think' means in this statement. The next part about understanding the concept I might very well not exist, is strange to me. If I don't exist, then how am I arguing with the person above? Anyways, I suppose it's more a question of personal identification than existence, because obviously statements counter to the presented notion of nihilism are being produced.